%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU681^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:44 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU681^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n013.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:09:07 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.29 % (2175564)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (2175571)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4264929030:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.29 % (2175571)Refutation not found, incomplete strategy
% 0.23/0.29 % (2175571)------------------------------
% 0.23/0.29 % (2175571)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (2175571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (2175571)CaDiCaL version: 2.1.3
% 0.23/0.29 % (2175571)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.29 % (2175571)Time elapsed: 0.001 s
% 0.23/0.29 % (2175571)Peak memory usage: 12 MB
% 0.23/0.29 % (2175571)Instructions burned: 3 (million)
% 0.23/0.29 % (2175571)------------------------------
% 0.23/0.29 % (2175571)------------------------------
% 0.23/0.29 % (2175575)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.29 % (2175575)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.29 % (2175569)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1138140557:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.29 % (2175570)lrs+10_16_si=on:nwc=1.5:random_seed=1366939901:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.29 % (2175572)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3420244110:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.29 % (2175573)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=79606352:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.29 % (2175574)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=812352446:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.29 % (2175575)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1353800786:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.29 % (2175569) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2175564-2175569"...
% 0.23/0.29 % (2175577)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2179253963:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.29 % (2175574) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2175564-2175574"...
% 0.23/0.29 % (2175577)Instruction limit reached!
% 0.23/0.29 % (2175577)------------------------------
% 0.23/0.29 % (2175577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (2175577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (2175577)CaDiCaL version: 2.1.3
% 0.23/0.29 % (2175577)Termination reason: Instruction limit
% 0.23/0.29 % (2175577)Termination phase: Saturation
% 0.23/0.29 % (2175577)Time elapsed: 0.001 s
% 0.23/0.29 % (2175577)Peak memory usage: 11 MB
% 0.23/0.29 % (2175577)Instructions burned: 3 (million)
% 0.23/0.29 % (2175569)...printing done.
% 0.23/0.29 % (2175569)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% 0.23/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.23/0.29 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.23/0.29 thf(func_def_2, type, subsetE: $o).
% 0.23/0.29 thf(func_def_4, type, kpair: ($i > $i > $i)).
% 0.23/0.29 thf(func_def_5, type, cartprod: ($i > $i > $i)).
% 0.23/0.29 thf(func_def_6, type, cartprodmempair1: $o).
% 0.23/0.29 thf(func_def_7, type, breln: ($i > $i > $i > $o)).
% 0.23/0.29 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.29 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.29 thf(func_def_17, type, sK3: ($i > $o)).
% 0.23/0.29 thf(func_def_19, type, sK5: ($i > $i > $i > $i)).
% 0.23/0.29 thf(func_def_20, type, sK6: ($i > $i > $i > $i)).
% 0.23/0.29 thf(func_def_27, type, vNOT: ($o > $o)).
% 0.23/0.29 thf(f1,axiom,(
% 0.23/0.29 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 0.23/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE)).
% 0.23/0.29 thf(f2,axiom,(
% 0.23/0.29 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X0 @ X1)) => ? [X3 : $i] : (? [X4 : $i] : ((X2 = ((kpair @ X3 @ X4))) & (in @ X4 @ X1)) & (in @ X3 @ X0))) = cartprodmempair1)),
% 0.23/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1)).
% 0.23/0.29 thf(f3,axiom,(
% 0.23/0.29 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2 @ (cartprod @ X0 @ X1)))))),
% 0.23/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
% 0.23/0.29 thf(f4,conjecture,(
% 0.23/0.29 subsetE => (cartprodmempair1 => ! [X2 : $i,X0 : $i,X1 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X4 : $i] : ((in @ X4 @ X2) => (X3 @ X4)))))),
% 0.23/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall1)).
% 0.23/0.29 thf(f5,negated_conjecture,(
% 0.23/0.29 ~(subsetE => (cartprodmempair1 => ! [X2 : $i,X0 : $i,X1 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X4 : $i] : ((in @ X4 @ X2) => (X3 @ X4))))))),
% 0.23/0.29 inference(negated_conjecture,[status(cth)],[f4])).
% 0.23/0.29 thf(f6,plain,(
% 0.23/0.29 ~(subsetE => (cartprodmempair1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X2 @ X0) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X0) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X0) => (X3 @ X6))))))),
% 0.23/0.29 inference(rectify,[],[f5])).
% 0.23/0.29 thf(f7,plain,(
% 0.23/0.29 ~((subsetE = $true) => ((cartprodmempair1 = $true) => ! [X1 : $i,X2 : $i,X0 : $i] : ((((breln @ X1 @ X2 @ X0)) = $true) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((((in @ X4 @ X1)) = $true) => ! [X5 : $i] : (($true = ((in @ X5 @ X2))) => (($true = ((in @ (kpair @ X4 @ X5) @ X0))) => (((X3 @ (kpair @ X4 @ X5))) = $true)))) => ! [X6 : $i] : (($true = ((in @ X6 @ X0))) => ($true = ((X3 @ X6))))))))),
% 0.23/0.29 inference(fool_elimination,[],[f6])).
% 0.23/0.29 thf(f8,plain,(
% 0.23/0.29 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.23/0.29 inference(fool_elimination,[],[f3])).
% 0.23/0.29 thf(f9,plain,(
% 0.23/0.29 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 0.23/0.29 inference(rectify,[],[f1])).
% 0.23/0.29 thf(f10,plain,(
% 0.23/0.29 (subsetE = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) => ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)))),
% 0.23/0.29 inference(fool_elimination,[],[f9])).
% 0.23/0.29 thf(f11,plain,(
% 0.23/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X1 @ X0)) => ? [X3 : $i] : (? [X4 : $i] : ((X2 = ((kpair @ X3 @ X4))) & (in @ X4 @ X0)) & (in @ X3 @ X1))) = cartprodmempair1)),
% 0.23/0.29 inference(rectify,[],[f2])).
% 0.23/0.29 thf(f12,plain,(
% 0.23/0.29 (cartprodmempair1 = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (($true = ((in @ X2 @ (cartprod @ X1 @ X0)))) => ? [X3 : $i] : (? [X4 : $i] : ((((in @ X4 @ X0)) = $true) & (((kpair @ X3 @ X4)) = X2)) & ($true = ((in @ X3 @ X1)))))),
% 0.23/0.29 inference(fool_elimination,[],[f11])).
% 0.23/0.29 thf(f13,plain,(
% 0.23/0.29 ! [X1 : $i,X2 : $i,X0 : $i] : (($true != ((in @ X2 @ (cartprod @ X1 @ X0)))) | ? [X3 : $i] : (? [X4 : $i] : ((((in @ X4 @ X0)) = $true) & (((kpair @ X3 @ X4)) = X2)) & ($true = ((in @ X3 @ X1))))) <=> (cartprodmempair1 = $true)),
% 0.23/0.29 inference(ennf_transformation,[],[f12])).
% 0.23/0.29 thf(f14,plain,(
% 0.23/0.29 (subsetE = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) | (((subset @ X0 @ X1)) != $true))),
% 0.23/0.29 inference(ennf_transformation,[],[f10])).
% 0.23/0.29 thf(f15,plain,(
% 0.23/0.29 ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((subset @ X0 @ X1)) != $true) | (((in @ X2 @ X0)) != $true)) <=> (subsetE = $true)),
% 0.23/0.29 inference(flattening,[],[f14])).
% 0.23/0.29 thf(f16,plain,(
% 0.23/0.29 (? [X1 : $i,X2 : $i,X0 : $i] : (? [X3 : ($i > $o)] : (? [X6 : $i] : (($true != ((X3 @ X6))) & ($true = ((in @ X6 @ X0)))) & ! [X4 : $i] : (! [X5 : $i] : (((((X3 @ (kpair @ X4 @ X5))) = $true) | ($true != ((in @ (kpair @ X4 @ X5) @ X0)))) | ($true != ((in @ X5 @ X2)))) | (((in @ X4 @ X1)) != $true))) & (((breln @ X1 @ X2 @ X0)) = $true)) & (cartprodmempair1 = $true)) & (subsetE = $true)),
% 0.23/0.29 inference(ennf_transformation,[],[f7])).
% 0.23/0.29 thf(f17,plain,(
% 0.23/0.29 (subsetE = $true) & (cartprodmempair1 = $true) & ? [X2 : $i,X1 : $i,X0 : $i] : (? [X3 : ($i > $o)] : (? [X6 : $i] : (($true != ((X3 @ X6))) & ($true = ((in @ X6 @ X0)))) & ! [X4 : $i] : (! [X5 : $i] : (($true != ((in @ (kpair @ X4 @ X5) @ X0))) | ($true != ((in @ X5 @ X2))) | (((X3 @ (kpair @ X4 @ X5))) = $true)) | (((in @ X4 @ X1)) != $true))) & (((breln @ X1 @ X2 @ X0)) = $true))),
% 0.23/0.29 inference(flattening,[],[f16])).
% 0.23/0.29 thf(f18,plain,(
% 0.23/0.29 (subsetE = $true) & (cartprodmempair1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : ($i > $o)] : (? [X4 : $i] : ((((X3 @ X4)) != $true) & (((in @ X4 @ X2)) = $true)) & ! [X5 : $i] : (! [X6 : $i] : (($true != ((in @ (kpair @ X5 @ X6) @ X2))) | ($true != ((in @ X6 @ X0))) | ($true = ((X3 @ (kpair @ X5 @ X6))))) | (((in @ X5 @ X1)) != $true))) & ($true = ((breln @ X1 @ X0 @ X2))))),
% 0.23/0.29 inference(rectify,[],[f17])).
% 0.23/0.29 thf(f19,plain,(
% 0.23/0.29 (subsetE = $true) & (cartprodmempair1 = $true) & (((($true != ((sK3 @ sK4))) & (((in @ sK4 @ sK2)) = $true)) & ! [X5 : $i] : (! [X6 : $i] : (($true != ((in @ (kpair @ X5 @ X6) @ sK2))) | ($true != ((in @ X6 @ sK0))) | ($true = ((sK3 @ (kpair @ X5 @ X6))))) | (((in @ X5 @ sK1)) != $true))) & ($true = ((breln @ sK1 @ sK0 @ sK2))))),
% 0.23/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f18])).
% 0.23/0.29 thf(f20,plain,(
% 0.23/0.29 (! [X1 : $i,X2 : $i,X0 : $i] : (($true != ((in @ X2 @ (cartprod @ X1 @ X0)))) | ? [X3 : $i] : (? [X4 : $i] : ((((in @ X4 @ X0)) = $true) & (((kpair @ X3 @ X4)) = X2)) & ($true = ((in @ X3 @ X1))))) | (cartprodmempair1 != $true)) & ((cartprodmempair1 = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (($true = ((in @ X2 @ (cartprod @ X1 @ X0)))) & ! [X3 : $i] : (! [X4 : $i] : ((((in @ X4 @ X0)) != $true) | (((kpair @ X3 @ X4)) != X2)) | ($true != ((in @ X3 @ X1))))))),
% 0.23/0.29 inference(nnf_transformation,[],[f13])).
% 0.23/0.29 thf(f21,plain,(
% 0.23/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | ? [X3 : $i] : (? [X4 : $i] : ((((in @ X4 @ X2)) = $true) & (((kpair @ X3 @ X4)) = X1)) & (((in @ X3 @ X0)) = $true))) | (cartprodmempair1 != $true)) & ((cartprodmempair1 = $true) | ? [X5 : $i,X6 : $i,X7 : $i] : (($true = ((in @ X6 @ (cartprod @ X5 @ X7)))) & ! [X8 : $i] : (! [X9 : $i] : (($true != ((in @ X9 @ X7))) | (((kpair @ X8 @ X9)) != X6)) | ($true != ((in @ X8 @ X5))))))),
% 0.23/0.29 inference(rectify,[],[f20])).
% 0.23/0.29 thf(f22,plain,(
% 0.23/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | ((($true = ((in @ (sK6 @ X2 @ X1 @ X0) @ X2))) & (((kpair @ (sK5 @ X2 @ X1 @ X0) @ (sK6 @ X2 @ X1 @ X0))) = X1)) & ($true = ((in @ (sK5 @ X2 @ X1 @ X0) @ X0))))) | (cartprodmempair1 != $true)) & ((cartprodmempair1 = $true) | ((((in @ sK8 @ (cartprod @ sK7 @ sK9))) = $true) & ! [X8 : $i] : (! [X9 : $i] : (($true != ((in @ X9 @ sK9))) | (((kpair @ X8 @ X9)) != sK8)) | ($true != ((in @ X8 @ sK7))))))),
% 0.23/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK7,sK8,sK9]),skolemize(X4,sK6 @ X2 @ X1 @ X0),skolemize(X4,sK6 @ X2 @ X1 @ X0),skolemize(X5,sK7),skolemize(X6,sK8),skolemize(X7,sK9)],[f21])).
% 0.23/0.29 thf(f23,plain,(
% 0.23/0.29 (! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((subset @ X0 @ X1)) != $true) | (((in @ X2 @ X0)) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((subset @ X0 @ X1)) = $true) & (((in @ X2 @ X0)) = $true)))),
% 0.23/0.29 inference(nnf_transformation,[],[f15])).
% 0.23/0.29 thf(f24,plain,(
% 0.23/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) | ($true != ((subset @ X1 @ X0))) | (((in @ X2 @ X1)) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ X3))) & ($true = ((subset @ X4 @ X3))) & ($true = ((in @ X5 @ X4)))))),
% 0.23/0.29 inference(rectify,[],[f23])).
% 0.23/0.29 thf(f25,plain,(
% 0.23/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) | ($true != ((subset @ X1 @ X0))) | (((in @ X2 @ X1)) != $true)) | (subsetE != $true)) & ((subsetE = $true) | (($true != ((in @ sK12 @ sK10))) & (((subset @ sK11 @ sK10)) = $true) & ($true = ((in @ sK12 @ sK11)))))),
% 0.23/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X3,sK10),skolemize(X4,sK11),skolemize(X5,sK12)],[f24])).
% 0.23/0.29 thf(f26,plain,(
% 0.23/0.29 ($true = ((breln @ sK1 @ sK0 @ sK2)))),
% 0.23/0.29 inference(cnf_transformation,[],[f19])).
% 0.23/0.29 thf(f27,plain,(
% 0.23/0.29 ( ! [X6 : $i,X5 : $i] : (($true != ((in @ (kpair @ X5 @ X6) @ sK2))) | (((in @ X5 @ sK1)) != $true) | ($true = ((sK3 @ (kpair @ X5 @ X6)))) | ($true != ((in @ X6 @ sK0)))) )),
% 0.23/0.29 inference(cnf_transformation,[],[f19])).
% 0.23/0.29 thf(f28,plain,(
% 0.23/0.29 (((in @ sK4 @ sK2)) = $true)),
% 0.23/0.29 inference(cnf_transformation,[],[f19])).
% 0.23/0.29 thf(f29,plain,(
% 0.23/0.29 ($true != ((sK3 @ sK4)))),
% 0.23/0.29 inference(cnf_transformation,[],[f19])).
% 0.23/0.29 thf(f30,plain,(
% 0.23/0.29 (cartprodmempair1 = $true)),
% 0.23/0.29 inference(cnf_transformation,[],[f19])).
% 0.23/0.29 thf(f31,plain,(
% 0.23/0.29 (subsetE = $true)),
% 0.23/0.29 inference(cnf_transformation,[],[f19])).
% 0.23/0.29 thf(f34,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | ($true = ((in @ (sK5 @ X2 @ X1 @ X0) @ X0))) | (cartprodmempair1 != $true)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f22])).
% 0.23/0.29 thf(f35,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | (((kpair @ (sK5 @ X2 @ X1 @ X0) @ (sK6 @ X2 @ X1 @ X0))) = X1) | (cartprodmempair1 != $true)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f22])).
% 0.23/0.29 thf(f36,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | ($true = ((in @ (sK6 @ X2 @ X1 @ X0) @ X2))) | (cartprodmempair1 != $true)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f22])).
% 0.23/0.29 thf(f40,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X0)) = $true) | ($true != ((subset @ X1 @ X0))) | (((in @ X2 @ X1)) != $true) | (subsetE != $true)) )),
% 0.23/0.29 inference(cnf_transformation,[],[f25])).
% 0.23/0.29 thf(f41,plain,(
% 0.23/0.29 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.23/0.29 inference(cnf_transformation,[],[f8])).
% 0.23/0.29 thf(f44,plain,(
% 0.23/0.29 ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ sK1 @ sK0 @ sK2)))),
% 0.23/0.29 inference(definition_unfolding,[],[f26,f41])).
% 0.23/0.29 thf(f45,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | ($true != $true) | ($true = ((in @ (sK6 @ X2 @ X1 @ X0) @ X2)))) )),
% 0.23/0.29 inference(definition_unfolding,[],[f36,f30])).
% 0.23/0.29 thf(f46,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | (((kpair @ (sK5 @ X2 @ X1 @ X0) @ (sK6 @ X2 @ X1 @ X0))) = X1) | ($true != $true)) )),
% 0.23/0.29 inference(definition_unfolding,[],[f35,f30])).
% 0.23/0.29 thf(f47,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | ($true != $true) | ($true = ((in @ (sK5 @ X2 @ X1 @ X0) @ X0)))) )),
% 0.23/0.29 inference(definition_unfolding,[],[f34,f30])).
% 0.23/0.29 thf(f50,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != ((subset @ X1 @ X0))) | (((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) )),
% 0.23/0.29 inference(definition_unfolding,[],[f40,f31])).
% 0.23/0.29 thf(f54,plain,(
% 0.23/0.29 ($true = ((subset @ sK2 @ (cartprod @ sK1 @ sK0))))),
% 0.23/0.29 inference(beta-eta_normalization,[],[f44])).
% 0.23/0.29 thf(f55,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | ($true = ((in @ (sK6 @ X2 @ X1 @ X0) @ X2)))) )),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f45])).
% 0.23/0.29 thf(f56,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | (((kpair @ (sK5 @ X2 @ X1 @ X0) @ (sK6 @ X2 @ X1 @ X0))) = X1)) )),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f46])).
% 0.23/0.29 thf(f57,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((subset @ X1 @ X0))) | (((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) )),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f50])).
% 0.23/0.29 thf(f58,plain,(
% 0.23/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (cartprod @ X0 @ X2))) != $true) | ($true = ((in @ (sK5 @ X2 @ X1 @ X0) @ X0)))) )),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f47])).
% 0.23/0.29 thf(f59,plain,(
% 0.23/0.29 ( ! [X0 : $i] : (($true = ((in @ X0 @ (cartprod @ sK1 @ sK0)))) | ($true != $true) | (((in @ X0 @ sK2)) != $true)) )),
% 0.23/0.29 inference(constrained_superposition,[],[f57,f54])).
% 0.23/0.29 thf(f60,plain,(
% 0.23/0.29 ( ! [X0 : $i] : ((((in @ X0 @ sK2)) != $true) | ($true = ((in @ X0 @ (cartprod @ sK1 @ sK0))))) )),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f59])).
% 0.23/0.29 thf(f61,plain,(
% 0.23/0.29 (((in @ sK4 @ (cartprod @ sK1 @ sK0))) = $true) | ($true != $true)),
% 0.23/0.29 inference(constrained_superposition,[],[f60,f28])).
% 0.23/0.29 thf(f62,plain,(
% 0.23/0.29 (((in @ sK4 @ (cartprod @ sK1 @ sK0))) = $true)),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f61])).
% 0.23/0.29 thf(f63,plain,(
% 0.23/0.29 ($true != $true) | ($true = ((in @ (sK6 @ sK0 @ sK4 @ sK1) @ sK0)))),
% 0.23/0.29 inference(constrained_superposition,[],[f55,f62])).
% 0.23/0.29 thf(f64,plain,(
% 0.23/0.29 ($true = ((in @ (sK6 @ sK0 @ sK4 @ sK1) @ sK0)))),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f63])).
% 0.23/0.29 thf(f65,plain,(
% 0.23/0.29 ($true = ((in @ (sK5 @ sK0 @ sK4 @ sK1) @ sK1))) | ($true != $true)),
% 0.23/0.29 inference(constrained_superposition,[],[f58,f62])).
% 0.23/0.29 thf(f66,plain,(
% 0.23/0.29 ($true = ((in @ (sK5 @ sK0 @ sK4 @ sK1) @ sK1)))),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f65])).
% 0.23/0.29 thf(f67,plain,(
% 0.23/0.29 ($true != $true) | (((kpair @ (sK5 @ sK0 @ sK4 @ sK1) @ (sK6 @ sK0 @ sK4 @ sK1))) = sK4)),
% 0.23/0.29 inference(constrained_superposition,[],[f56,f62])).
% 0.23/0.29 thf(f68,plain,(
% 0.23/0.29 (((kpair @ (sK5 @ sK0 @ sK4 @ sK1) @ (sK6 @ sK0 @ sK4 @ sK1))) = sK4)),
% 0.23/0.29 inference(trivial_inequality_removal,[],[f67])).
% 0.23/0.29 thf(f69,plain,(
% 0.23/0.29 (((in @ sK4 @ sK2)) != $true) | ($true = ((sK3 @ sK4))) | ($true != ((in @ (sK5 @ sK0 @ sK4 @ sK1) @ sK1))) | ($true != ((in @ (sK6 @ sK0 @ sK4 @ sK1) @ sK0)))),
% 0.23/0.29 inference(constrained_superposition,[],[f27,f68])).
% 0.23/0.29 thf(f70,plain,(
% 0.23/0.29 ($true != ((in @ (sK6 @ sK0 @ sK4 @ sK1) @ sK0))) | ($true != ((in @ (sK5 @ sK0 @ sK4 @ sK1) @ sK1))) | ($true = ((sK3 @ sK4)))),
% 0.23/0.29 inference(forward_subsumption_resolution,[],[f69,f28])).
% 0.23/0.29 thf(f71,plain,(
% 0.23/0.29 ($true = ((sK3 @ sK4))) | ($true != ((in @ (sK5 @ sK0 @ sK4 @ sK1) @ sK1)))),
% 0.23/0.29 inference(forward_subsumption_resolution,[],[f70,f64])).
% 0.23/0.29 thf(f72,plain,(
% 0.23/0.29 ($true != ((in @ (sK5 @ sK0 @ sK4 @ sK1) @ sK1)))),
% 0.23/0.29 inference(forward_subsumption_resolution,[],[f71,f29])).
% 0.23/0.29 thf(f73,plain,(
% 0.23/0.29 $false),
% 0.23/0.29 inference(forward_subsumption_resolution,[],[f72,f66])).
% 0.23/0.29 % SZS output end Proof for theBenchmark
% 0.23/0.29 % (2175569)------------------------------
% 0.23/0.29 % (2175569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (2175569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (2175569)CaDiCaL version: 2.1.3
% 0.23/0.29 % (2175569)Termination reason: Refutation
% 0.23/0.29 % (2175569)Time elapsed: 0.006 s
% 0.23/0.29 % (2175569)Peak memory usage: 12 MB
% 0.23/0.29 % (2175569)Instructions burned: 9 (million)
% 0.23/0.29 % (2175564)Success in time 0.029 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------